Acta Applicandae Mathematicae

, Volume 112, Issue 3, pp 263–274

# Modeling of Free Convection Boundary Layer Flow on a Solid Sphere with Newtonian Heating

Article

## Abstract

In this paper, the mathematical model of free convection boundary layer flow on a solid sphere with Newtonian heating, in which the heat transfer from the surface is proportional to the local surface temperature, is considered. The transformed boundary layer equations are solved numerically using an efficient numerical scheme known as the Keller-box method. Numerical solutions are obtained for the local wall temperature, the local skin friction coefficient, as well as the velocity and temperature profiles. The features of the flow and heat transfer characteristics for different values of the Prandtl number Pr and conjugate parameter γ are analyzed and discussed.

### Keywords

Boundary layer Free convection Solid sphere Newtonian heating Numerical solutions

## Preview

### References

1. 1.
Chiang, T., Ossin, A., Tien, C.L.: Laminar free convection from a sphere. J. Heat Transf. 86C, 537–542 (1964) Google Scholar
2. 2.
Amato, W.S., Tien, C.: Free convection heat transfer from isothermal spheres in water. Int. J. Heat Mass Transf. 15, 327–339 (1972)
3. 3.
Huang, M.J., Chen, C.K.: Laminar free convection from a sphere with blowing and suction. J. Heat Transf. 109, 529–532 (1987)
4. 4.
Chen, T.S., Mucoglu, A.: Analysis of mixed forced and free convection about a sphere. Int. J. Heat Mass Transf. 20, 867–875 (1977)
5. 5.
Jafarpur, K., Yovanovich, M.M.: Laminar free convection heat transfer from isothermal spheres: a new analytical method. Int. J. Heat Mass Transf. 35, 2195–2201 (1992)
6. 6.
Jia, H., Gogos, G.: Laminar natural convection heat transfer from isothermal spheres. Int. J. Heat Mass Transf. 39(8), 1603–1615 (1996)
7. 7.
Nazar, R., Amin, N., Grosan, T., Pop, I.: Free convection boundary layer on an isothermal sphere in a micropolar fluids. Int. Commun. Heat Mass Transf. 29(3), 377–386 (2002)
8. 8.
Nazar, R., Amin, N., Grosan, T., Pop, I.: Free convection boundary layer on an isothermal sphere with constant surface heat flux in a micropolar fluids. Int. Commun. Heat Mass Transf. 29(8), 1129–1138 (2002)
9. 9.
Nazar, R., Amin, N., Pop, I.: On the mixed convection boundary layer flow about a solid sphere with constant surface temperature. Arab. J. Sci. Eng. 27(2C), 119–135 (2002) Google Scholar
10. 10.
Molla, M.M., Hossain, M.A.: Effects of chemical reaction, heat and mass diffusion in natural convection flow from and isothermal sphere with temperature dependent viscosity. Int. J. Comput.-Aided Eng. Softw. 23, 840–857 (2006)
11. 11.
Cheng, C.Y.: Natural convection heat and mass transfer from a sphere in micropolar fluids with constant wall temperature and concentration. Int. Commun. Heat Mass Transf. 35, 750–755 (2008)
12. 12.
Merkin, J.H.: Natural convection boundary-layer flow on a vertical surface with Newtonian Heating. Int. J. Heat Fluid Flow 15, 392–398 (1994)
13. 13.
Lesnic, D., Ingham, D.B., Pop, I.: Free convection boundary layer flow along a vertical surface in a porous medium with Newtonian heating. Int. J. Heat Mass Transf. 42, 2621–2627 (1999)
14. 14.
Lesnic, D., Ingham, D.B., Pop, I.: Free convection from a horizontal surface in a porous medium with Newtonian heating. J. Porous Media 3, 227–235 (2000)
15. 15.
Lesnic, D., Ingham, D.B., Pop, I., Storr, C.: Free convection boundary layer flow above a nearly horizontal surface in a porous medium with Newtonian heating. Heat Mass Transf. 40, 665–672 (2004)
16. 16.
Pop, I., Lesnic, D., Ingham, D.B.: Asymptotic solutions for the free convection boundary-layer flow along a vertical surface in a porous medium with Newtonian heating. Hybrid Methods Eng. 2, 31–40 (2000) Google Scholar
17. 17.
Chaundary, R.C., Preeti, Jain: Unsteady free convection boundary-layer flow past an impulsively started vertical surface with Newtonian heating. Rom. J. Phys. 9, 911–925 (2006) Google Scholar
18. 18.
Chaundary, R.C., Preeti, Jain: An exact solution to the unsteady free convection boundary-layer flow past an impulsively started vertical surface with Newtonian heating. J. Eng. Phys. Thermophys. 80, 954–960 (2007)
19. 19.
Salleh, M.Z., Nazar, R., Pop, I.: Forced convection boundary layer flow at a forward stagnation point with Newtonian heating. Chem. Eng. Commun. 196, 987–996 (2009)
20. 20.
Salleh, M.Z., Nazar, R., Pop, I.: Mixed convection boundary layer flow over a horizontal circular cylinder with Newtonian heating. Heat Mass Transf. (2010, accepted) Google Scholar
21. 21.
Salleh, M.Z., Nazar, R.: Free convection boundary layer flow over a horizontal circular cylinder with Newtonian heating. Sains Malays. 39(4) (2010, in press) Google Scholar
22. 22.
Salleh, M.Z., Nazar, R., Pop, I.: Boundary layer flow and heat transfer over a stretching sheet with Newtonian heating. J. Taiwan Inst. Chem. Eng. (2010). doi: Google Scholar
23. 23.
Luikov, A.V., Aleksashenko, V.A., Aleksashenko, A.A.: Analytic methods of solution of conjugate problems in convection heat transfer. Int. J. Heat Mass Transf. 14, 1047–1056 (1971)
24. 24.
Martynenko, O.G., Khramtsov, P.P.: Free-Convective Heat Transfer. Springer, Berlin (2005) Google Scholar
25. 25.
Na, T.Y.: Computational Methods in Engineering Boundary Value Problem. Academic Press, New York (1979) Google Scholar
26. 26.
Cebeci, T., Bradshaw, P.: Physical and Computational Aspects of Convective Heat Transfer. Springer, New York (1988)
27. 27.
Cebeci, T., Cousteix, J.: Modeling and Computation of Boundary-Layer Flows: Laminar, Turbulent and Transitional Boundary Layers in Incompressible and Compressible Flows. Springer, Berlin (2005) Google Scholar
28. 28.
Salleh, M.Z., Nazar, R., Arifin, N.M., Pop, I., Merkin, J.H.: Forced convection heat transfer over a horizontal circular cylinder with Newtonian heating. J. Eng. Math. (2009, submitted) Google Scholar
29. 29.
Salleh, M.Z., Ahmad, S., Nazar, R.: Numerical solutions of the forced convection boundary layer flow at a forward stagnation point. Eur. J. Sci. Res. 19, 644–653 (2008) Google Scholar